Solve for $t$, $ -\dfrac{5}{6t} = \dfrac{t + 5}{2t} + \dfrac{1}{4t} $
First we need to find a common denominator for all the expressions. This means finding the least common multiple of $6t$ $2t$ and $4t$ The common denominator is $12t$ To get $12t$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ -\dfrac{5}{6t} \times \dfrac{2}{2} = -\dfrac{10}{12t} $ To get $12t$ in the denominator of the second term, multiply it by $\frac{6}{6}$ $ \dfrac{t + 5}{2t} \times \dfrac{6}{6} = \dfrac{6t + 30}{12t} $ To get $12t$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ \dfrac{1}{4t} \times \dfrac{3}{3} = \dfrac{3}{12t} $ This give us: $ -\dfrac{10}{12t} = \dfrac{6t + 30}{12t} + \dfrac{3}{12t} $ If we multiply both sides of the equation by $12t$ , we get: $ -10 = 6t + 30 + 3$ $ -10 = 6t + 33$ $ -43 = 6t $ $ t = -\dfrac{43}{6}$